4.10. Evolution along the Hubble sequence and growth of the black hole
Non-axisymmetric instabilities like bars force the galaxies to evolve towards large mass concentrations, large bulge-to-disk ratios, lower gas content through consumption by star formation. This means that a galaxy born as a late-type, will progressively evolve towards early-types, with a somewhat chaotic path, from barred to unbarred, and sometimes moving backwards, when the disk accretes mass. The gross lines of this evolution are sketched in fig 14.
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Figure 14. Cartoon of galaxy evolution along the Hubble sequence. A galaxy, with a small mass distributed mainly in a disk, without bulge (late-type), is unstable with respect to spiral and bar formation (steps 1 and 2). The bar drives the gas towards the center, and the bulge is building up (see in each frame the edge-on projection). When there is too much mass concentrated in the center, the bar is destroyed (step 4), and the gas coming from the outer parts, enrich the disk, and re-establish a larger disk to bulge ratio. Later on (steps 5 and 6), another bar will form, when the disk to bulge ratio is favorable. A secondary bar (cf step 3) may help the primary one to drive the mass towards the center. At the end, the galaxy may be classified early-type. |
To summarize this bar-driven evolution, and gather the main features obtained through N-body simulations, and supported by observations, it is interesting to test a toy model, in a semi-analytical way, including:
- star formation, with a combination of a quiescent rate, proportional to the gas density, in a time scale of 3 Gyr, and a bar-driven contribution, with a threshold (Q < 1) and a rate equal to (1 - Q) / t*, with t*, the star-formation time-scale (proportional to the dynamical time-scale for gravitational instabilities).
- radial flows: when a bar is formed, gravity torques
produce gas inflow, therefore with a threshold
Q < 1 also, and rate (1 - Q) / tvis,
with tvis, the ``gravitational viscosity'' time-scale,
~ 1 / 
(Mtot
/ Md)2.
- bulge formation: the inflowing gas (and stars) are assumed to form the bulge through star-formation and vertical resonances
- death of bars: when Q > 1 (central concentrations, lack of gas and self-gravitating disk)
- gas infall: possibility of a continuous small infall or a periodically substantial one (from companions).
- black hole formation: a fixed fraction beff of the radial gas flow is taken to contribute to its formation, i.e. dMbh / dt = beff Mg(1 - Q) / tvis, with a threshold Q < 1.
Figure 15 displays some results of the toy model (Combes, 2000). The most striking feature is the self-regulation of the stability parameter Q towards 1. Although the galaxy initially starts almost completely gaseous, the gas mass fraction soon stabilises to 10% of the total. Also the mass of the central concentration (or black hole) stabilises to a constant fraction of the bulge mass, as observed (Magorrian et al. 1998).
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Figure 15. Model of periodic gas accretion in a galaxy with star formation, birth and death of bars, radial flows and black hole formation taken into account: Top left Full line: gas mass versus time; dash line: gas mass fraction. Top middle Full line: stellar mass; dash lines: disk stellar mass at top, and bottom bulge mass. Top right Full line: total mass; dash lines: total disk mass at top, and bottom bulge mass. Bottom left Disk star formation rate versus time. Bottom middle Toomre Q parameter. Bottom right Full line: mass of the central black hole, and dash line: mass ratio between the black hole and the bulge. |